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1: 19.2 Definitions
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►where is a polynomial in while and are rational functions of .
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►Here are real parameters, and and are real or complex variables, with , .
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►If , then is pure imaginary.
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§19.2(iv) A Related Function:
… ►For the special cases of and see (19.6.15). …2: 34.6 Definition: Symbol
3: 34.7 Basic Properties: Symbol
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34.7.1
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►Odd permutations of columns or rows introduce a phase factor , where is the sum of all arguments of the symbol.
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34.7.2
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34.7.3
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34.7.5
4: 32.3 Graphics
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►Plots of solutions of with and for various values of , and the parabola .
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►Here is the solution of with and such that
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►Here is the solution of
…The corresponding solution of is given by
…with , , and
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5: 10.48 Graphs
6: 3.4 Differentiation
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►The are the differentiated Lagrangian interpolation coefficients:
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►where and .
►For the values of and used in the formulas below
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►For partial derivatives we use the notation .
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7: 4.17 Special Values and Limits
8: 16.12 Products
9: 27.2 Functions
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►Functions in this section derive their properties from the fundamental
theorem of arithmetic, which states that every integer can be represented uniquely as a product of prime powers,
…where are the distinct prime factors of , each exponent is positive, and is the number of distinct primes dividing .
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►Note that .
►In the following examples, are the exponents in the factorization of in (27.2.1).
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►Table 27.2.2 tabulates the Euler totient function , the divisor function (), and the sum of the divisors (), for .
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